Knife
One of the most common types of carving knives is the paring knife. It employs a forefinger-to-thumb motion like peeling an apple. You'll find, with carving, you'll want one that fits you perfectly. You may want several for specific uses. Cut the contour of the blade and tang from the band saw blade with a cutoff wheel. Sandwich the tang between two pieces of hardwood. Carve or file the wood to fit your hand, then sharpen the blade with a fine grinding wheel. Hone it with jewelers rouge and a buffing wheel.
Simple Scrapers
Scrapers are under-utilized woodworking tools, perhaps because they're not understood. A scraper performs functions similar to a block plane. It just works very differently. Rather than slicing wood like a plane, the scraper levels wood surfaces perpendicularly. Scrapers must be sharp with a blade set at 90 degrees. They'll become rounded over with use, so you have to re-sharpen then with files or sharpening stones.
Contour Scrapers
If a flat scraper is underutilized, a contour scraper is even more so. They're great tools, though, and band saw blades are ideal sources of material. You use a contour scraper the way you would use a router bit, but rather than relying on it to create an entire contour, you can use it to sharpen fine details, like making a very crisp, ornamental bead. Just file the inverse shape into the flat stock and mount a handle on it, like a dough knife.
Small, Concave or Convex Spokeshaves
Generally, spokeshaves -- cousins to the block-plane -- use thicker steel than found in even an industrial band saw blade. But band saw stock will work for small ones if the span of the blade is small enough you won't encounter too much blade-flex in the relatively thin metal. Since the band saw blade is flexible, you can use it to make a concave or convex spokeshave, bowing the blade in or out to match the contour of your homemade spokeshave deck.